Pluricomplex energy classes associated to a positive closed current

Abstract

The aim of this paper is to extend the domain of definition of $(d{d}^c\cdot {)}^q\wedge T$ on some classes of plurisubharmonic (psh) functions, which are not necessary bounded, where $T$ is a positive closed current of bidimension $(q,q)$ on an open set $\Omega$ of ${\mathbb{C}}^n$. We introduce two classes ${\mathcal{F}}_p^T(\Omega )$ and ${\mathcal{E}}_p^T(\Omega )$ and we show that they belong to the domain of definition of the operator $(d{d}^c\cdot {)}^q\wedge T$. We also prove that all functions belong to these classes are $C_T$-quasicontinuous and that the comparison principle is valid in them.